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31
Stacked area chart with percentage option, axes flipped
Percentiles
For each percentile p, plots the value y such that p percent of the points are smaller than y. Two
popular methods are included. For a percentile p, the rank is computed according to k=p(n+1)/100,
and the value that corresponds to that rank taken. In the rounding method, k is rounded to the
nearest integer, while in the interpolation method, non-integer ranks are handled by linear
interpolation between the two nearest ranks.
Missing values are deleted.
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Normal probability plot
Plots a normal probability (normal QQ) plot for one column of data. A normal distribution will plot on
a straight line. For comparison, an RMA regression line is given, together with the Probability Plot
Correlation Coefficient.
(three groups were given in this example)
Missing values are deleted.
The normal order statistic medians are computed as N(i) = G(U(i)), where G is the inverse of the
cumulative normal distribution function and U are the uniform order statistic medians:
i n
n
i
n
i
i
U n
U i
1n
0.5
1
2,3,...
0.365
3175
0.
1
( ),
1
()
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Ternary
Ternary plot for three columns of data, normally containing proportions of compositions.  If a fourth
column is included, it will be shown using either a bubble representation or as a color/grayscale map.
Rows with missing value(s) in any column are deleted. When using the color map option, rows with
only the fourth variable missing are included in the plot but do not contribute to the map.
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34
Bubble plot
Plotting 3D data (three columns) by showing the third axis as size of disks. Negative values are not
shown. Select "Subtract min" to subtract the smallest third axis value from all values - this will force
the data to be positive. The "Size" slider scales the bubbles relative to unit radius on the x axis scale.
Rows with missing value(s) in any column are deleted.
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35
Matrix
Two-dimensional plot of the data matrix, using a grayscale with white for lowest value, black for
highest, or a colour scale. Includes contouring. Use to get an overview over a large data matrix.
Missing values are plotted as blanks (allowing holes and non-square boundaries).
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36
Surface
Three-dimensional landscape plot of a data matrix of elevation values. Colors are assigned according
to height, and/or the surface can be gray-shaded using a lighting model. Vertical exaggeration is
adjustable. Missing values are replaced with the average. The data in the example below are the
same as for the matrix plot above.
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37
3D scatter/bubble plot
Requires three or four columns of data. For three columns, the data are plotted as fixed-size spheres
with the given xyz coordinates. An optional fourth column is shown as sizes of bubbles. The
coordinate system is right-handed, with the z axis vertical (positive up). Sticks can be added to
emphasize the positions in the xy plane.
38
Univariate
This function computes a number of basic descriptive statistics for one or more samples (columns) of
univariate data. Each sample must have at least 3 values.  The columns can have different numbers
of values.
The following numbers are shown for each sample:
N:
The number of values n in the sample
Min:
The minimum value
Max:
The maximum value
Mean:
The estimate of the mean, calculated as
n
x
x
i
Std. error:
The standard error of the estimate of the mean, calculated as
n
s
SE
x
where s is the estimate of the standard deviation (see below).
39
Variance:
The sample variance, calculated as
2
2
1
1
x x
n
s
i
Stand. dev.:  The sample standard deviation, calculated as
2
1
1
x
x
n
s
i
Median:
The median of the sample. For n odd, the given value such that there are equally
many values above and below. For n even, the average of the two central values.
25 prcntil:
The 25
th
percentile, i.e. the given value such that 25% of the sample is below, 75%
above. The ͞interpolation͟ method is used ;see Percentile plot aboveͿ.
75 prcntil:
The 75
th
percentile, i.e. the given value such that 75% of the sample is below, 25%
above.  The ͞interpolation͟ method is used ;see Percentile plot aboveͿ.
Skewness:
The sample skewness, zero for a normal distribution, positive for a tail to the right.
Calculated as
3
2
3
1
1
1
2)
( 1)(
x
x
n
x
x
n
n
n
G
i
i
Note there are several versions of this around – Past uses the same equation as SPSS
and Excel. Slightly different results may occur using other programs, especially for
small sample sizes.
Kurtosis:
The sample kurtosis, zero for a normal distribution. Calculated as



3
2
1
3
1
1
3
2
1
1
2
4
2
4
2
n
n
n
x x
n
x
x
n
n
n
nn
G
i
i
Again Past uses the same equation as SPSS and Excel.
Geom. mean:  The geometric mean, calculated as
n
n
x
xx
1/
1 2
. Logarithms are used internally.
Coeff.var:
Coefficient of variation, or ratio of standard deviation to the mean, in percent:
100
1
1
100
2
 
x
x
x
n
x
s
CV
i